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Optimal emission-extraction policy in a world of scarcity and irreversibility
[Politique optimale d'émission/extraction dans dans un monde de rareté et d’irréversibilité]

Author

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  • Fabien Prieur

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UPVM - Université Paul-Valéry - Montpellier 3 - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier, UM1 - Université Montpellier 1)

  • Mabel Tidball

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UPVM - Université Paul-Valéry - Montpellier 3 - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

Abstract

This paper extends the classical exhaustible-resource/stock-pollution model with the irreversibility of pollution decay. Within this framework, we are wondering first how the potential irreversibility of pollution affects the extraction path. Our aim is also to emphasize the conditions under which the economy will optimally adopt a reversible policy. Once the situation has turned irreversible, we show that the pollution problem does affect the total amount of resource extracted. In particular, it may be optimal to leave a positive amount of resource in the ground forever. As far the optimal extraction/emission policy is concerned, three types of solutions may arise. We derive a simple condition that guarantees that it is optimal to stay in what is called the reversible region. When this condition does not hold, it is difficult to conclude whether the optimal policy is reversible or irreversible. Using a numerical example, one can find a situation where the optimal path is unique and identify the set of initial conditions associated with each possible policy. Due to the non-convexity introduced by the decay function, the occurrence of multiple optimal solutions cannot be ruled out. Indeed, we present another numerical example in which two optimality candidates – one being reversible, the other irreversible – simultaneously exist. The computation of the present values of both paths reveals that the reversible policy yields the highest value.

Suggested Citation

  • Fabien Prieur & Mabel Tidball, 2011. "Optimal emission-extraction policy in a world of scarcity and irreversibility [Politique optimale d'émission/extraction dans dans un monde de rareté et d’irréversibilité]," Post-Print hal-02807037, HAL.
  • Handle: RePEc:hal:journl:hal-02807037
    Note: View the original document on HAL open archive server: https://hal.inrae.fr/hal-02807037
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    1. Raouf Boucekkine & Aude Pommeret & Fabien Prieur, 2013. "Technological vs. Ecological Switch and the Environmental Kuznets Curve," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 95(2), pages 252-260.
    2. Polasky, Stephen & de Zeeuw, Aart & Wagener, Florian, 2011. "Optimal management with potential regime shifts," Journal of Environmental Economics and Management, Elsevier, vol. 62(2), pages 229-240, September.
    3. Sinclair, Peter J N, 1994. "On the Optimum Trend of Fossil Fuel Taxation," Oxford Economic Papers, Oxford University Press, vol. 46(0), pages 869-877, Supplemen.
    4. Alain Ayong Le Kama & Aude Pommeret & Fabien Prieur, 2014. "Optimal Emission Policy under the Risk of Irreversible Pollution," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 16(6), pages 959-980, December.
    5. Tsur, Yacov & Zemel, Amos, 2005. "Scarcity, growth and R&D," Journal of Environmental Economics and Management, Elsevier, vol. 49(3), pages 484-499, May.
    6. Hoel, Michael & Karp, Larry, 2002. "Taxes versus quotas for a stock pollutant," Resource and Energy Economics, Elsevier, vol. 24(4), pages 367-384, November.
    7. Renaud Coulomb & Fanny Henriet, 2010. "Carbon price and optimal extraction of a polluting fossil fuel with restricted carbon capture," Working Papers halshs-00564852, HAL.
    8. van der Ploeg, Frederick & Withagen, Cees, 2012. "Is there really a green paradox?," Journal of Environmental Economics and Management, Elsevier, vol. 64(3), pages 342-363.
    9. Barbier, Edward B. & Markandya, Anil, 1990. "The conditions for achieving environmentally sustainable development," European Economic Review, Elsevier, vol. 34(2-3), pages 659-669, May.
    10. Raouf Boucekkine & Aude Pommeret & Fabien Prieur, 2013. "Technological vs. Ecological Switch and the Environmental Kuznets Curve," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 95(2), pages 252-260.
    11. Chakravorty, Ujjayant & Magne, Bertrand & Moreaux, Michel, 2006. "A Hotelling model with a ceiling on the stock of pollution," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2875-2904, December.
    12. Larry Karp & Jiangfeng Zhang, 2016. "Taxes Versus Quantities for a Stock Pollutant with Endogenous Abatement Costs and Asymmetric Information," Studies in Economic Theory, in: Graciela Chichilnisky & Armon Rezai (ed.), The Economics of the Global Environment, pages 493-533, Springer.
    13. Dietz, Simon & Asheim, Geir B., 2012. "Climate policy under sustainable discounted utilitarianism," Journal of Environmental Economics and Management, Elsevier, vol. 63(3), pages 321-335.
    14. Sinclair, P.J.N., 1994. "On the Optimum Trend of Fossil Fuel Taxation," Discussion Papers 94-16, Department of Economics, University of Birmingham.
    15. Tsur, Yacov & Zemel, Amos, 2002. "The Regulation of Environmental Innovations," Journal of Environmental Economics and Management, Elsevier, vol. 44(2), pages 242-260, September.
    16. Amigues, Jean-Pierre & Moreaux, Michel, 2013. "The atmospheric carbon resilience problem: A theoretical analysis," Resource and Energy Economics, Elsevier, vol. 35(4), pages 618-636.
    17. Chakravorty, Ujjayant & Krulce, Darrell L, 1994. "Heterogeneous Demand and Order of Resource Extraction," Econometrica, Econometric Society, vol. 62(6), pages 1445-1452, November.
    18. C. G. Plourde, 1972. "A Model of Waste Accumulation and Disposal," Canadian Journal of Economics, Canadian Economics Association, vol. 5(1), pages 119-125, February.
    19. Amigues, Jean-Pierre & Moreaux, Michel, 2012. "Potential Irreversible Catastrophic Shifts of the Assimilative Capacity of the Environment," LERNA Working Papers 12.01.358, LERNA, University of Toulouse.
    20. Rüdiger Pethig, 1992. "Ecological Dynamics and the Valuation of Environmental Change," Volkswirtschaftliche Diskussionsbeiträge 37-92, Universität Siegen, Fakultät Wirtschaftswissenschaften, Wirtschaftsinformatik und Wirtschaftsrecht.
    21. Hoel, Michael, 1983. "Monopoly resource extractions under the presence of predetermined substitute production," Journal of Economic Theory, Elsevier, vol. 30(1), pages 201-212, June.
    22. Hoel, Michael & Kverndokk, Snorre, 1996. "Depletion of fossil fuels and the impacts of global warming," Resource and Energy Economics, Elsevier, vol. 18(2), pages 115-136, June.
    23. Ujjayant Chakravorty & Michel Moreaux & Mabel Tidball, 2008. "Ordering the Extraction of Polluting Nonrenewable Resources," American Economic Review, American Economic Association, vol. 98(3), pages 1128-1144, June.
    24. Tsur, Yacov & Zemel, Amos, 2003. "Optimal transition to backstop substitutes for nonrenewable resources," Journal of Economic Dynamics and Control, Elsevier, vol. 27(4), pages 551-572, February.
    25. Tahvonen, Olli & Withagen, Cees, 1996. "Optimality of irreversible pollution accumulation," Journal of Economic Dynamics and Control, Elsevier, vol. 20(9-10), pages 1775-1795.
    26. Crépin, Anne-Sophie & Biggs, Reinette & Polasky, Stephen & Troell, Max & de Zeeuw, Aart, 2012. "Regime shifts and management," Ecological Economics, Elsevier, vol. 84(C), pages 15-22.
    27. Olli Tahvonen, 1997. "Fossil Fuels, Stock Externalities, and Backstop Technology," Canadian Journal of Economics, Canadian Economics Association, vol. 30(4), pages 855-874, November.
    28. Yacov Tsur & Amos Zemel, 2008. "Regulating environmental threats," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 39(3), pages 297-310, March.
    29. R. C. D'Arge & K. C. Kogiku, 1973. "Economic Growth and the Environment," Review of Economic Studies, Oxford University Press, vol. 40(1), pages 61-77.
    30. Larry Karp & Jiangfeng Zhang, 2005. "Regulation of Stock Externalities with Correlated Abatement Costs," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 32(2), pages 273-300, October.
    31. Forster, Bruce A., 1975. "Optimal pollution control with a nonconstant exponential rate of decay," Journal of Environmental Economics and Management, Elsevier, vol. 2(1), pages 1-6, September.
    32. Withagen, Cees, 1994. "Pollution and exhaustibility of fossil fuels," Resource and Energy Economics, Elsevier, vol. 16(3), pages 235-242, August.
    33. Frederick Ploeg & Cees Withagen, 2014. "Growth, Renewables, And The Optimal Carbon Tax," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 283-311, February.
    34. Liski, Matti, 2002. "Taxing average emissions to overcome the shutdown problem," Journal of Public Economics, Elsevier, vol. 85(3), pages 363-384, September.
    35. Gerard Gaudet & Michel Moreaux & Stephen W. Salant, 2001. "Intertemporal Depletion of Resource Sites by Spatially Distributed Users," American Economic Review, American Economic Association, vol. 91(4), pages 1149-1159, September.
    36. Ulph, Alistair & Ulph, David, 1994. "The Optimal Time Path of a Carbon Tax," Oxford Economic Papers, Oxford University Press, vol. 46(0), pages 857-868, Supplemen.
    37. Cropper, M. L., 1976. "Regulating activities with catastrophic environmental effects," Journal of Environmental Economics and Management, Elsevier, vol. 3(1), pages 1-15, June.
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    Cited by:

    1. Bonneuil, N. & Boucekkine, R., 2016. "Optimal transition to renewable energy with threshold of irreversible pollution," European Journal of Operational Research, Elsevier, vol. 248(1), pages 257-262.
    2. Raouf Boucekkine & Aude Pommeret & Fabien Prieur, 2012. "Optimal Regime Switching and Threshold Effects: Theory and Application to a Resource Extraction Problem under Irreversibility," Working Papers 12-14, LAMETA, Universtiy of Montpellier, revised May 2012.
    3. Alain Ayong Le Kama & Aude Pommeret & Fabien Prieur, 2014. "Optimal Emission Policy under the Risk of Irreversible Pollution," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 16(6), pages 959-980, December.
    4. Prudence Dato, 2017. "Energy Transition Under Irreversibility: A Two-Sector Approach," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 68(3), pages 797-820, November.
    5. Amigues, Jean-Pierre & Moreaux, Michel, 2013. "The atmospheric carbon resilience problem: A theoretical analysis," Resource and Energy Economics, Elsevier, vol. 35(4), pages 618-636.
    6. Ngo Van Long & Fabien Prieur & Klarizze Puzon & Mabel Tidball, 2013. "Markov Perfect Equilibria in Differential Games with Regime Switching Strategies," Working Papers 13-06, LAMETA, Universtiy of Montpellier, revised Jan 2014.
    7. Cassin, Lesly & Melindi-Ghidi, Paolo & Prieur, Fabien, 2022. "Confronting climate change: Adaptation vs. migration in Small Island Developing States," Resource and Energy Economics, Elsevier, vol. 69(C).
    8. Fouad El Ouardighi & Hassan Benchekroun & Dieter Grass, 2016. "Self-regenerating environmental absorption efficiency and the $$\varvec{ soylent~green~scenario}$$ s o y l e n t g r e e n s c e n a r i o," Annals of Operations Research, Springer, vol. 238(1), pages 179-198, March.
    9. Amigues, Jean-Pierre & Moreaux, Michel, 2012. "Potential Irreversible Catastrophic Shifts of the Assimilative Capacity of the Environment," LERNA Working Papers 12.01.358, LERNA, University of Toulouse.
    10. van der Ploeg, Frederick, 2014. "Abrupt positive feedback and the social cost of carbon," European Economic Review, Elsevier, vol. 67(C), pages 28-41.
    11. Daria Onori, 2015. "Optimal Growth and Debt Dynamics under GDP-Based Collaterals," Working Papers halshs-01251352, HAL.
    12. Stahn, Hubert & Tomini, Agnes, 2021. "Externality and common-pool resources: The case of artesian aquifers," Journal of Environmental Economics and Management, Elsevier, vol. 109(C).
    13. Marc Chesney & Pierre Lasserre & Bruno Troja, 2017. "Mitigating global warming: a real options approach," Annals of Operations Research, Springer, vol. 255(1), pages 465-506, August.
    14. van der Ploeg, Frederick, 2014. "Abrupt positive feedback and the social cost of carbon," European Economic Review, Elsevier, vol. 67(C), pages 28-41.

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    More about this item

    Keywords

    non-renewable resource; optimal policy; irreversible pollution; emission polluante;
    All these keywords.

    JEL classification:

    • Q30 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - General
    • Q53 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Air Pollution; Water Pollution; Noise; Hazardous Waste; Solid Waste; Recycling
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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